If the period of the function f(x) = sin 5x c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the function $f(x) = \sin 5x \cos 3x$. Using the trigonometric identity $2 \sin A \cos B = \sin(A+B) + \sin(A-B)$,we can rewrite the functio

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(D) Given the function $f(x) = \sin 5x \cos 3x$. Using the trigonometric identity $2 \sin A \cos B = \sin(A+B) + \sin(A-B)$,we can rewrite the function as: $f(x) = \frac{1}{2} [\sin(5x+3x) + \sin(5x-3x)] = \frac{1}{2} (\sin 8x + \sin 2x)$. The period of $\sin 8x$ is $T_1 = \frac{2\pi}{8} = \frac{\pi}{4}$. The period of $\sin 2x$ is $T_2 = \frac{2\pi}{2} = \pi$. The period of the sum of two periodic functions is the Least Common Multiple ($L$.$C$.$M$.) of their individual periods. $\alpha = 	ext{L.C.M.}\left(\frac{\pi}{4}, \piight) = \frac{	ext{L.C.M.}(\pi, \pi)}{	ext{H.C.F.}(4, 1)} = \frac{\pi}{1} = \pi$. Thus,$\alpha = \pi$. Finally,$\cos \alpha = \cos \pi = -1$.

If the period of the function $f(x) = \sin 5x \cos 3x$ is $\alpha$,then $\cos \alpha =$

Similar Questions

Which of the following functions has a period of $2\pi$?

Let $f(x) = \sin x + \cos(ax)$ be a periodic function. Then:

The period of the function $\sin \left( \frac{\pi x}{2} \right) + \cos \left( \frac{\pi x}{2} \right)$ is

The period of $\sin ^4 x + \cos ^4 x$ is

The period of the function $f(x) = \frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right) - 5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module